True or False
In order for the distribution of sample means to be normal, it must be based on samples of at least n = 30 scores.
TRUE
False.
The statement is commonly known as the "Central Limit Theorem Misconception." The Central Limit Theorem states that as the sample size increases, the distribution of sample means approaches a normal distribution, regardless of the shape of the population distribution. However, there is no specific threshold such as n = 30 that determines when the distribution of sample means becomes normal.
To understand this concept, one can conduct a simulation.
1. Define a population distribution: Determine a population distribution that is not normal, such as a uniform or skewed distribution.
2. Sample: Take multiple samples of varying sizes (e.g., n = 10, n = 20, n = 50).
3. Calculate sample means: Calculate the mean for each sample.
4. Repeat: Repeat steps 2 and 3 numerous times to obtain a sufficient number of sample means.
5. Plot the distribution of sample means: Create a histogram or dot plot of the sample means.
By doing so, it will be evident that as the sample size increases, the distribution of sample means becomes more normal in shape, regardless of the initial population distribution. However, even with smaller sample sizes, the distribution of sample means will still exhibit certain characteristics of normality due to the Central Limit Theorem.